 
Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & SpringerVerlag
Zbl 1042.22005
Anandavardhanan, U.K.; Prasad, Dipendra
Distinguished representations for SL(2). (English)
Math. Res. Lett. 10, No. 56, 867878 (2003). ISSN 10732780
http://www.mathjournals.org/mrl/
A representation of a group G is said to be distinguished with respect to a subgroup
H of G if it admits a nontrivial Hinvariant linear form, i.e., there exists a linear form
on V such that ((h)v) = (v) for all h H and v V.
This work is on distinguished representations of the group G = SL2(E) with respect to
the subgroup H = SL2(F), where E/F is a quadratic extension of padic fields. Denote
by HomH(, 1) the space of Hinvariant linear forms. The authors classify distinguished
representations and compute the dimension of HomH(, 1). Possible dimensions are 1,
2 and 4, in contrast to the results for (GLn(E), GLn(F)), where the space of invariant
forms is at most onedimensional. They show that the dimension of HomH(, 1) varies
inside an Lpacket similar in spirit to the multiplicity formula for automorphic repre
sentations due to J.P. Labesse and R. P. Langlands [Can. J. Math. 31, 726785 (1979;
Zbl 0421.12014)].
Their approach is based on the structure of Lpackets and the results for (GL2(E), GL2(F))
